We all know that Nunu is a pretty strong support pick due to pure utility from BB. However, I've always found it interesting that both support Nunu and jungle Nunu tend to build the same (ie GP10 into utility items, Aegis, etc). Why don't support Nunus aggressively counterjungle like jungle Nunu does?

A support Nunu plus a quick-clearing jungler, say Mundo, could guarantee early enemy buff control, as consume smite tankiness would be pretty difficult to contend with for a solo jungler. Furthermore, if you have an AD with an escape, such as Ez, your bottom lane should be fine for the brief periods of time when Nunu leaves to aid your jungler. Finally, an early point in consume allows a support Nunu to steal wolves, wraiths, and golems by himself, though wraiths are probably the only "safe" camp to steal early game.

Considering this lane swap meta, I'm envisioning a composition like the following:

Send Nunu/AD (Ez?) mid, to allow Nunu to counterjungle more aggressively

Send a "safe" AP mid (Vlad, Kennen) top

Send a strong 2v1 champ (Yorick?) bottom

Whatever jungler you want

What would be the weaknesses of a team composition centered around a counterjungling support?

DISCLAIMER - I'm level 21, so I may or may not really know what I'm talking about. I do enjoy theorycrafting, though.